## Class Work 28 Nov 2012

### Permutation Problems

**Q. 1: **
A secretary writes letters to A, B, C, and D. She also prepares four
envelopes addressed to A, B, C, and D. She manages to put *all*
the letters in the wrong envelopes. Enumerate (list) all the ways she
can do that.

**Q. 2: **
You have the following books that you would like to arrange on your
book shelf.

- War and Peace by Leo Tolstoy
- Anna Karenina by Leo Tolstoy
- Magic Mountain by Thomas Mann
- Death in Venice by Thomas Mann
- Arms and the Man by Bernard Shaw
- Candida by Bernard Shaw

Enumerate the different ways you can arrange the books as long as you
keep the books by the same author together.
**Q. 3: **
A, B, C, D, E go to a ball game. A and B want to sit next to each other
but C and D prefer not to. Enumerate the different ways that they can
sit on the same bench.

### Combination Problems

**Q. 4: **
Home owners A, B, C, D, E, and F have all agreed to serve on the
home owners' association. But the home owners' association just
needs three people. A is willing to serve only if B serves,
though B has not made that same condition. C and D both refuse to
serve if the other is on the committee. Enumerate the different
committees that you can form.

**Q. 5: **
A side show at Coney Island is described as follows: There were ten
little dummies which you were to knock over with baseballs. The man
said: "Take as many throws as you like at a cent apiece and stand
as close as you please. Add up the numbers on all the men that
you knock down and when the sum amounts to exactly fifty, neither
more nor less you get a genuine 25 cent Maggie Cline cigar with a
gold band around it."

The numbers on the ten dummies were 15, 9, 30, 21, 19, 3, 12, 6,
25, and 27.

**Q. 6:**
Given a set of integers create two subsets such that the sum of
numbers in one subset is roughly equal to the sum of the numbers
in the other subset. All elements in the set must be in either
one subset or the other.